Question

A wheel rotating with uniform angular acceleration covers 50 revolutions in the first five seconds after the start, Find the angular acceleration and the angular velocity at the end of five seconds?

Answer 1

 Given in the question :-
θ = 50
time t = 5 sec.

Now by the equation of kinematics,

$\theta = \omega t + \frac{1}{2} \alpha t^2$
Putting the values in this formula
50 = 0 + 1/2 α x 5²
⇒25α = 100
⇒α = 4 revolution/s²


Now assume that after 5 second angular velocity will be ω'. then the equation will be

$\omega' = \omega + \alpha t$

On putting the values.
ω= 0 + 4 x 5

ω =20 revolition/s. 



Hope it Helps :-)

Answer 2

The angular acceleration is α = 4 revolution/s², and the angular velocity at the end of five seconds is ω = 20 revolution/s.

Explanation:

Step 1 :

Given values in the question  

A spinning wheel with uniform angular acceleration covers 50 turns in the first five seconds following start

It mean,

           θ = 50

           time t = 5 sec.

Step 2 :

Now by the kinematics equation,

                                $\theta=w t+\frac{1}{2} \alpha t^{2}$

Substitute, the values in the formula  

                              $50=0+\frac{1}{2} \alpha 5^{2}$

                             $50=0+\frac{1}{2} \times \alpha \times 25$

                             $50=\frac{1}{2} \times 25 \alpha$

                            $100=25 \alpha$

                            $\alpha=\frac{100}{25}$

                          α = 4 revolution/s²

Step 3 :

Now, assume that the angular velocity after 5 seconds will be equal to the velocity. That's the equation.

                             w’=w+ αt

When the values are set.

                           ω= 0 + 4 x 5

                          ω = 20 revolution/s.    

Hence, the angular acceleration is α = 4 revolution/s² , and the angular velocity at the end of five seconds is ω = 20 revolution/s.